Automated NNLL+NLO Resummation for Jet-Veto Cross Sections

TL;DR

Jet-veto cross sections in electroweak-boson production are enhanced by Sudakov logs of $p_T^{veto}/Q$. The authors automate NNLL resummation and fixed-order matching using a factorization formula with hard functions $\mathcal{H}_{ij}$ and beam functions $\bar{B}_i$, implemented in MadGraph5_aMC@NLO, and propose two schemes to combine resummation with NLO results. Phenomenological results for $Z$ and $W^+W^-$ production at the LHC show improved perturbative stability and good agreement with fixed-order results, with small matching corrections, while illustrating the benefits and limitations of resummation in the presence of experimental cuts and leptonic decays. This automated framework paves the way for higher-order resummations across a wider class of vector-boson final states, with potential extensions to include two-loop effects, gluon-induced channels, and jet-final-state processes.

Abstract

In electroweak-boson production processes with a jet veto, higher-order corrections are enhanced by logarithms of the veto scale over the invariant mass of the boson system. In this paper, we resum these Sudakov logarithms at next-to-next-to-leading logarithmic (NNLL) accuracy and match our predictions to next-to-leading order (NLO) fixed-order results. We perform the calculation in an automated way, for arbitrary electroweak final states and in the presence of kinematic cuts on the leptons produced in the decays of the electroweak bosons. The resummation is based on a factorization theorem for the cross sections into hard functions, which encode the virtual corrections to the boson production process, and beam functions, which describe the low-p_T emissions collinear to the beams. The one-loop hard functions for arbitrary processes are calculated using the MadGraph5_aMC@NLO framework, while the beam functions are process independent. We perform the resummation for a variety of processes, in particular for W+W- pair production followed by leptonic decays of the W bosons.

Figures (9)

• Figure 1: Structure and kinematics of the factorization theorem for the $W^+ W^-$ production cross section in the presence of a jet veto.
• Figure 2: Resummed cross sections for $Z$-boson production (top) and $W^+ W^-$ pair production (bottom) obtained at NLL (red) and NNLL (blue) order. The bands are obtained by varying the hard matching scale $\mu_h$ and the factorization scale $\mu$ by factors of 2 about their default values $|\mu_h|=Q$ and $\mu=p_T^{\space\rm veto}\space$. The gray bands show the fixed-order NLO results with scale variation $\mu_r=\mu_f\in[p_T^{\space\rm veto}\space/2,\,2Q]$ for comparison. The panels on the left refer to the standard choice $\mu_h^2>0$, while those on the right show results obtained using $\mu_h^2<0$.
• Figure 3: Left: NLO predictions for the $W^+ W^-$ production cross section obtained with a conservative estimate of scale uncertainties (grey), and with scale variations about high (green) and low (magenta) default values; see text for further information. Right: Kinematic distribution in the variable $Q$ of the leading-order cross section.
• Figure 4: Resummed and matched predictions for the $W^+ W^-$ production cross section (obtained by varying the matching scale about the default value $\mu_m=p_T^{\space\rm veto}\space$ and $\mu_m=Q$) compared with the fixed-order result at NLO. The panels below the plots indicate the relative size of the power-suppressed matching corrections at NNLL order.
• Figure 5: Left: Comparison of the resummed and matched NNLL+NLO predictions for the $W^+ W^-$ cross section obtained in Scheme A (additive matching) with Scheme B (multiplicative matching). Right: Comparison of the NNLL+NLO predictions with the NLO result matched to Pythia using aMC@NLO.